The Shapes Game is a great way to "break the ice" in the first week of a Geometry class. The teacher asks the students to work in groups of 3 or 4 students, usually the ones already sitting nearby. Then the teacher hands out a "shapes card" (see below) to one person in each group, asking them to be sure they do not show it to any other member of the group. There are 5 different pages included here, each one with the same shapes but in different positions, so the groups will have different ones. The shapes on all handouts are square, isosceles right triangle, equilateral triangle, circle, and half-circle.
The student holding the paper will describe the objects out loud, and the members of the group are supposed to draw what is described. The students should not look at each other's papers, and of course not see the paper help by the "reader". As the"reader" describes each shape and it's location, the other students in his or her group will draw the shapes as they are described. Students take turns being the "reader".
Students should be encouraged to use mathematical terminology such as square, rectangle, circle, diameter, triangle, horizontal, vertical, rotate, 45 degrees, 90 degrees, congruent, diagonal, etc. Perhaps the teacher or a student might write these words on the board, either before, after, or during the game.
For example, a student might describe the shapes on their paper as follows:
"First draw half of a circle with the curved part on top. Then at the bottom right corner of the half circle shape, draw a triangle that has a right angle, and 2 sides equal. Draw that triangle with one of the points of a smaller angle touching the bottom right part of the half circle.
The students can ask the reader questions, and all students should use mathematical terminology whenever possible. No one is allowed to look at anyone else's drawing until the end of the game. When all the drawings are complete, and only then, the student holding the original drawing can show it to the group. The students or the teacher can decide whose solution best matches the drawing on the original handout. It is up to the teacher whether scoring and prizes might be included in the game.
There are many benefits to this game. Students will start to get to know each other, if they don't know each other already. They will hear, and use, mathematical terminology. But perhaps the most important thing they will learn, and the reason behind the game, is that they realize the importance of clear and correct terminology: this will begin the foundation for success in Geometry.
Here is an example of what two of the "shapes cards" might look like:
If a student had shape number one above, she might describe it to her partner as follows: "There are 5 shapes, and the are all different. The top left figure is an isosceles right triangle, with the right angle vertex at the top left so that one of the legs of the triangle is vertical and the other leg is horizontal. A circle is below that triangle, attached to the isosceles triangle at its lowest vertex. At the right vertex of the horizontal leg of the isosceles triangle, a square is attached, with the top side of the square horizontal and aligned with the top line of the isosceles triangle . . . etc.
Correct mathematical definitions and descriptions are essential, and students playing this game will soon realize the value of precise terminology. This is, of course, the purpose of the game!